Solve for $r$, $ \dfrac{9}{15r + 25} = -\dfrac{r - 5}{12r + 20} - \dfrac{3}{6r + 10} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $15r + 25$ $12r + 20$ and $6r + 10$ The common denominator is $60r + 100$ To get $60r + 100$ in the denominator of the first term, multiply it by $\frac{4}{4}$ $ \dfrac{9}{15r + 25} \times \dfrac{4}{4} = \dfrac{36}{60r + 100} $ To get $60r + 100$ in the denominator of the second term, multiply it by $\frac{5}{5}$ $ -\dfrac{r - 5}{12r + 20} \times \dfrac{5}{5} = -\dfrac{5r - 25}{60r + 100} $ To get $60r + 100$ in the denominator of the third term, multiply it by $\frac{10}{10}$ $ -\dfrac{3}{6r + 10} \times \dfrac{10}{10} = -\dfrac{30}{60r + 100} $ This give us: $ \dfrac{36}{60r + 100} = -\dfrac{5r - 25}{60r + 100} - \dfrac{30}{60r + 100} $ If we multiply both sides of the equation by $60r + 100$ , we get: $ 36 = -5r + 25 - 30$ $ 36 = -5r - 5$ $ 41 = -5r $ $ r = -\dfrac{41}{5}$